等差数列在等差数列an中,已知公
在等差数列an中，已知公差d?0，前n项和为Sn，且满足a2×a3 = 45，a1 + a4 = 14。若bn = Sn÷(n + c)且bn为等差数列,求非零常数。
a1 + a4 = 14
(a2 - d) + (a3 + d) = 14
a2 + a3 = 14
a2×a3 = 45
联立、，并解得
a2 = 5，a3 = 9
d = 4
a1 = 5 - 4 = 1
S1 = a1 = 1
S2 = S1 + a2 = 6
S3 = S2 + a3 = 15
。 。。。。。
b1 = S1/(1 + c) = 1/(1 + c)
b2 = S2/(2 + c) = 6/(2 + ...全部
在等差数列an中，已知公差d?0，前n项和为Sn，且满足a2×a3 = 45，a1 + a4 = 14。若bn = Sn÷(n + c)且bn为等差数列,求非零常数。
a1 + a4 = 14
(a2 - d) + (a3 + d) = 14
a2 + a3 = 14
a2×a3 = 45
联立、，并解得
a2 = 5，a3 = 9
d = 4
a1 = 5 - 4 = 1
S1 = a1 = 1
S2 = S1 + a2 = 6
S3 = S2 + a3 = 15
。
。。。。。
b1 = S1/(1 + c) = 1/(1 + c)
b2 = S2/(2 + c) = 6/(2 + c)
b3 = S3/(3 + c) = 15/(3 + c)
。
。。。。。
2×b2 = b1 + b3
2×6/(2 + c) = 1/(1 + c) + 15/(3 + c)
12(1 + c)(3 + c) = (2 + c)(3 + c) + 15(1 + c)(2 + c)
12c^2 + 48c + 36 = c^2 + 5c + 6 + 15c^2 + 45c + 30
4c^2 + 2c = 0
2c^2 + c = 0
c(2c + 1) = 0
c = -1/2
_____________________________
b1 = 1/(1 - 1/2) = 2
b2 = 6/(2 - 1/2) = 4
b3 = 15/(3 - 1/2) = 6
。
。。。。。
由此可见，{bn}是首项为2，公差也为2的等差数列。收起
